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Question
Find the value of a, b, c and d from the equation:
`[(a - b, 2a + c),(2a - b, 3c + d)] = [(-1, 5),(0, 13)]`
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Solution
`[(a - b, 2a + c),(2a - b, 3c + d)] = [(-1, 5),(0, 13)]`
As the two matrices are equal, their corresponding elements are also equal.
Comparing the corresponding elements, we get:
a – b = –1 ...(1)
2a – b = 0 ...(2)
2a + c = 5 ...(3)
3c + d = 13 ...(4)
From (2), we have:
b = 2a
Then, from (1), we have:
a – 2a = –1
⇒ a = 1
⇒ b = 2
Now, from (3), we have:
2 × 1 + c = 5
⇒ c = 3
From (4) we have:
3 × 3 + d = 13
⇒ 9 + d = 13
⇒ d = 4
∴ a = 1, b = 2, c = 3 and d = 4
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